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<H2><A NAME="SECTION001254000000000000000">
Single sideband modulation</A>
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<P>
<DIV ALIGN="CENTER"><A NAME="fig08.31"></A><A NAME="10628"></A>
<TABLE>
<CAPTION ALIGN="BOTTOM"><STRONG>Figure 8.31:</STRONG>
Using an all-pass filter network to
make a frequency shifter.
</CAPTION>
<TR><TD><IMG
WIDTH="506" HEIGHT="289" BORDER="0"
SRC="img1026.png"
ALT="\begin{figure}\psfig{file=figs/fig08.31.ps}\end{figure}"></TD></TR>
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<P>
As described in Section <A HREF="node154.html#sect8.singlesideband">8.4.3</A>, a pair of all-pass filters
can be constructed to give roughly <IMG
WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img5.png"
ALT="$\pi /2$"> phase difference for positive
frequencies and <IMG
WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
SRC="img283.png"
ALT="$-\pi/2$"> for negative ones. The design of these pairs is
beyond the scope of this discussion (see, for instance, [<A
HREF="node202.html#r-mitra93">Reg93</A>]) but
Pd does provide an abstraction, <TT>hilbert~</TT>, to do this. Example
H09.ssb.modulation.pd, shown in Figure <A HREF="#fig08.31">8.31</A>, demonstrates how to use the
<TT>hilbert~</TT> abstraction to do signal sideband modulation. The
Hilbert transform dates to the analog era [<A
HREF="node202.html#r-strange72">Str95</A>, pp.129-132].
<P>
The two outputs of <TT>hilbert~</TT>, considered as the real and imaginary parts
of a complex-valued signal, are multiplied by a complex sinusoid (at
right in the figure), and the real part is output. The components of the
resulting signal are those of the input shifted by a (positive or negative)
frequency specified in the number box.
<P>
<BR><HR>
<ADDRESS>
Miller Puckette
2006-12-30
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